It is a neat sheet, and can hardly fail of meeting with a most hearty welcome from teachers, advanced pupils, and many business and professional men who either have little time for thoroughly reading the newspapers, or wish to preserve a record of events in a condensed and convenient form. It is worth more than its price to any family.- Daily Republican, Monongahela City, Pa." CURRENT TOPICS. The Educator reaches teachers in New York State a few days before each examination, giving them the latest matter on" Current Topics." We want 60,000 SUBSCRIBERS before the end of the year. Therefore until April 30th, 1894, orders from schools in clubs of not less than 10 names will be filled at 25 cents for each yearly subscription, to that great current topic paper THE EDUCATOR. After that date no orders will be received at less than one SINGLE SUBSCRIPTION RATE. 50 CENTS A YEAR. Send card to "The Educator," 10 Exchange St., Buffalo, N. Y., for samples and information telling how to use the paper for SUPPLEMENTARY READING and in HISTORY and CIVIL GOVERNMENT CLASSES. It is now used in hundreds of the best schools. SUPPLEMENTARY READING. I prize The Educator for it turns the mind of young people away from sensational and vicious reading to the reading of brief and clearly-put statements of things that are really important.-J. M. DAVIS, Ph.D., Pres. Rio Grande College, Rio Grande, O. A WOMAN'S SUCCESS WIFE Fortwo years I have made $25 a week at Home. Instructions FREE to lady readers. Send stamp. (No humbug.) MRS. J. A. MANNING, Box 69, ANNA, OHIO. CANNOT SEE HOW YOU DU MY IT AND PAY FREIGHT. Buy the Oxford Improved SINGER Sewing Machine, with a complete set of attachments and guaranteed for 10 years Shipped any where on 30 days' trial. No money required in ad vance. 75,000 now in use. World's Fair Medal awarded. Buy from factory, save dealers' and agents' profit Write to-day for our LARGE FREE CATALOGUE OXFORD $10.50 Oxford Mfg. Co., 342 Wabash Ave., Chicago, Ill HC. WHITCOMB & CO. ELECTROTYPERS. 42 ARCH STREET BOSTON NOTES. A FRIEND of the late actor, Edwin Booth, says that he was always bright, very fond of telling stories, but dreaded to receive calls that demanded dignity and ceremony. He liked rather to have around him some old friend or boon companion with whom he would chat and joke endlessly. HERE is a description of Sir Walter Scott as he appeared in 1807, written by an acquaintance of the great novelist: "This proudest boast of the Caledonian muses is tall and rather robust than slender, but lame. Neither the contour of his face nor features is elegant. His complexion is healthy and somewhat fair, without bloom. We find the singularity of brown hair and eyelashes with flaxen eyebrows, and a countenance open, ingenuous and benevolent. His eyes are of a lightish gray, deep thought on their lids; when seriously conversing he contracts his brows. An upper lip too long prevents his mouth from being decidedly handsome. His conversation is an overflowing fountain of brilliant wit, apposite allusion and playfull archness, while on serious themes it is nervous and eloquent; the accent decidedly Scotch, yet by no means broad. CONSUMPTION is averted, or if too late to avert it it is often cured and always relieved by Scott's Emulsion the Cream of Cod-liver Oil. Cures Coughs, Colds and Weak Lungs. Physicians, the world over, endorse it. Don't be deceived by Substitutes! Prepared by Scott & Bowne, N. Y. All Druggists No Stultifying Rules IN The Popular Educator Arithmetics. Hundreds and hundreds of practical problems all graded- but an infinite variety is the especial feature in which the POPULAR EDUCATOR ARITHMETICS excell all others. Books I and II. Price, 30 cents each. EDUCATIONAL PUBLISHING CO., 50 Bromfield St., Boston. EDUCATIONAL PUBLISHING CO., 50 Bromfield Street, Boston. 70 Fifth Avenue, New York. 262 Wabash Avenue, Chicago. POPULAR EDUCATOR Volume XI POPULAR EDUCATOR PUBLISHED BY THE A Magazine of Education February, 1894 EDUCATIONAL PUBLISHING COMPANY 50 BROMFIELD STREET, BOSTON NEW YORK OFFICE, 70 FIFTH AVENUE WESTERN OFFICE, 262 WABASH AVENUE, CHICAGO Published Monthly, September to June, Inclusive Subscription: $1.00 per year Single copies 10 cents Entered at the Post Office, Boston, Mass., as Second Class Matter A person without sufficient will should never try to govern children. Add to this kindliness of heart, and you have a teacher able to control the most unruly. Secretary Dickinson has resigned. Now, ladies and gents of the Board of Education, we want no "goody-goody," no dilettante to succeed him. Give us some one who has rich, red blood in every artery of his intellectual corpus; in other words, give us a man, if you please. Mark Hopkins on the end of the log is the essential thing. But such as he do not spring up in abundance in any one locality. The refusal of our school boards to recognize the fact is, to say the least, a monumental folly. Worth Considering. We earnestly recommend the reader's perusal of the article by Prof. Dewey of Ann Arbor, on the teaching of number to the young child. It is a radical departure. Is it not about time for the good of the child that a change in the method of approach to the young mind be made? We fear that the tyranny of the Grube system, even with the modifications that have been made, has had the tendency to stultify the brighter minds among the little folks. To force an active, intelligent mind of six years' growth to hover around 10 for a whole year may suit the conceit of the dry-as-dust pedant, but what about the condition of the child's mind after such a working in a peck measure, even if, in consequence of such a training, he thoroughly "knows ten?" The Freedom of the Teacher. Col. Parker has the courage of his convictions. We have found occasion to criticize him at times for his tendency to hyperbole, but he fights in the open, and he takes delight, we sometimes think, in battling against odds. In another part of this issue will be found a characteristic paper by the Colonel, well worth reading, and some of it should be taken to heart. Col. Parker is right when he says that the "essential preparation of teachers for their work must be made in the school-room and must be their personal experience;" and his reply to the question often put, "Is there not great danger in allowing teachers Number 6 to experiment on children?" is pertinent. "Not a tithe of the danger," he says, "there is in allowing supervisors to prescribe methods and rigidly enforce the literal following of a cours of study." He does not argue the question, but to us the reason is obvious. The chief value of the teacher in the school-room lies in the influence he has over the thoughts and feelings of the pupil. Again, to the degree that the teacher is above the mediocre in intellect, to that degree he is ambitious to be master and not s rvant. This is true in every other sphere of action as well. It is well that it should be so, and one only battles against the stars when he tries to resist it. Right here lies the curse of a supervision, bit of superintendent, school-board, or principal, that 'prescribes methods and rigidly enforces the literal following of a course of study." If the positions in the public schools are to be filled in the future, as in the past, by men and women of ability, then must supervision respect the freedom of the individual mind. It is only the other day that a very wise old gentleman, one who was a successful teacher in the forties, in the higher as well as lower courts of learning, and who, until recently has supervised the schools of a large city, said to us that he would not now advise a young man to prepare himself for a public school teacher. He himself had never felt the shoe pinch, but he had seen that article acting so offensively in these latter years, that he had come to the conclusion that teaching was not the best vocation for a young man of brighter parts to pursue. For the good of the children, however, we trust that the positions of influence in the schools will not be made less attractive to young men and women of ability. And we are glad to see the Colonel serving with us in the struggle against so vicious a tendency. A Valuable Report. The work of the committee of ten appointed a year or two ago by the National Teachers' Association to consider the work that should be required in the primary and secondary schools, is now before the country. On the following page we give the course of study recommended. We have space here to give only the changes recommended in mathematics and modern languages these being, too, the salient points, unless we except the curtailing of the work now done in geography. In arithmetic the committee recommend that the following subjects be curtailed or entirely omitted:-compound proportion, cube root, abstract mensuration, obsolete denominate quantities and the greater part of commercial arithmetic. As most schools in the more intelligent centers have already discarded all these subjects save the commercial arithmetic, it will be interesting to the reader only to know just what part of commercial arithmetic the committee desire to be taught. Here is what they say: It may be well that those pupils of our business colleges who are mature enough to understand such subjects as banking, insur ance, discount, partial payments, equation of payments, and the other branches commonly included under the term commercia arithmetic, and who have no expectation of taking any other mathematical course than this, should study these subjects exhaustively. But the case is different with pupils who are going through the courses of our regular graded schools. For them the subjects in question have no practical value, for the reason that they are too young and inexperienced to understand the principles on which business is conducted, and therefore waste valuable mental energy in fruitless struggles with problems which they cannot comprehend. In the text-books we find the subjects in question prefaced by very excellent definitions. The pupil who masters them will be able to state on examination that 'the market value of stock is what the stock brings per share when sold for cash'; that stock is at a discount when its market value is less than its par value'; that its par value is that named in the certificate'; that "the payee of a bill of exchange is the person to whom the money is ordered to be paid': in fine, to state in brief sentences the first principles of commercial law. He may also, after much conjecturing, be able to solve many questions in banking, exchange, insurance, and customhouse business. But until he is brought into actual contact with the business itself, he can form no clear conception of what it all means, or what are the uses or applications of the problems he is solving. On the other hand, when he is once brought face to face with business as an actuality; when for the first time he becomes a depositor in a savings bank, or a purchaser of shares in a corporation, he will find all the arithmetic necessary for his purposes to be interest, discount and percentage. The conceptions which he vainly endeavored to master by recitations from a text-book take their places in his mind with hardly the necessity of an effort on his part." It will be seen by our readers that this committee of experts are on the same ground that the POPULAR EDUCATOR has always taken. Speaking of Algebra, the committee think that the teacher may advantageously introduce the simple equation, and that the designation of positive integral powers by exponents may be taught; and this in connection with arithmetic in the grammar schools. The Committee would begin the geometrical work in the kindergarten and lower primary grades through drawing and modelling. At about the age of ten, the Committee recommend that one hour a week be devoted to the facts of plane and solid geometry and to familiarizing the pupils with these geometrical conceptions to be subsequently employed in abstract reasoning. The Committee would place in the grammar grades the study of either the French or German language. They advise that five recitation periods per week be given during the first year, at least four during the second, and at least three during the other two years. The objects to be obtained in these four years, according to the Committee, are: (1) a good pronunciation; (2) ability to understand very easy German and French when it is spoken; (3) to read, without painful effort, simple stories in the foreign language; (4) ability to construct short German or French sentences. Course of Study Recommended by the Committee of Ten,- Pres. Eliot, Chairman. 6. PHYSICS, CHEMISTRY, AND ASTRONOMY. 7. NATURAL HISTORY. Arithmetic during first eight years, with algebraic expressions and symbols and simple equations -no specific number of hours being recoinmended. Concrete Geometry, Concrete Geometry, 1 p. a wk. 1 p. a wk, Concrete Geometry 1 p. a wk. Concrete Geometry, 1 p. a wk. Study the natural phenomena 5 p. a wk. through first eight years by experiments, including physical measurements and the recommendations of Conferences 7 and 9. Throngh first eight years 2 p. a wk., of not less than 30 minutes each, devoted to plants and animals; the instruction to be correlated with language, drawing, literature, and geography. 8. HISTORY. 9. GEOGRAPHY. - the earth, Time alloted in first eight years to equal that given to number work. The subject - Abbreviations: p. a recitation period of 40-45 minutes; wk. = week; yr. = year. Physical Geography. The Pshychology of Number, as a BY PROF. JOHN DEWEY, University of Michigan. SOMETIMES wonder that there is not a strong reaction against the talk of the usefulness of psychology to the teacher much is nothing but talk. If psychology were required to justify itself by its fruits, I sometimes fear it would have little to say for itself. Perhaps some day a strong, successful teacher will arise in public and utter remarks of the following sort: "After suppressing my feelings for a number of years, from fear of the contempt I should call down on myself, I now wish to speak frankly my mind. The current deification of psychology for the teacher is a fraud. Psychology has become a fetich, which is worshipped with no knowledge of the why or wherefore. It has become a superstition. If we dared open our eyes, see and speak for ourselves, we should all acknowledge that we had got next to nothing from it; that whatever in it is helpful is not because it is psychology, but because it is good common sense, while whatever in it is psychology, is not helpful, but is the repetition of vague generalities, worn out precepts, and fine-sounding phrases which everyone repeats, but which are so very general that no one acts upon thein." Now I am a phychologist myself by profession, and am not, therefore, likely to propagate any such heresy. Yet I should not be much surprised to hear such talk growing more frequent — and I should not be much grieved. There is enough truth in it to warrant a challenge to the psychologist to come out and justify himself in the region of concrete methods to come out from the shelter of generalities about proceeding from the concrete to the abstract, and state what, on psychological grounds, would be the proper way to teach, in detail, e.g., elementary writing. I should like to see him forced from descriptions of imagination, assertions of its importance, hints as to training of it to be obtained from geography, to a detailed statement of what geography is, considered as a psychological fact. I think it would be good for the psychologist as well as helpful to the teacher. I have no doubt that there was a missionary period in which it was necessary to preach the importance of psychology in general, without much descent into detail. I have no doubt that the general precepts to which I have alluded played their part in getting rid of errors and in making ready the ground for a sowing of more fertile seed. But if, (as seems to be the case) this missionary work has succeeded, the need is now to take up special fields of instruction and to show just what is the bearing of psychology upon each of them: - what psychology has to say, for example, concerning teaching history, the selection of material, of methods of presentation, of questioning and investigation appropriate to different periods of child-life; the aims, intellectual and moral to be attained, and all this as detailed as possible and still be in psychological language. In this article, I do not intend to do this for arithmetic, but I do intend, to the best of my ability, to show what number, in its main relations and operations is, as a psychological fact, and thus point out the conditions to which any method of instruction must conform in order to be true to the child's mind, and thus accomplish the most with the least waste. If I do not succeed wholly to the reader's satisfaction, I desire him to bear in mind that while there is plenty of abstract mathematical discussion on one side, and plenty of concrete "method" of teaching on the other, there is little enough which attempts to connect those methods with the fundamental properties of number, to say nothing of putting them on a psychological basis. I suppose the first question that will arise in anyone's mind is this:- What is meant by saying that number and numerical prop*Copyrighted, 1894, by EDUCATIONAL PUBLISHING COMPANY. erties are psychological? Number, it would seem, is a quality of things, and while a pshychical operation may be required to abstract it from things, and to manipulate it after it has been derived, this is very different from saying that number itself is a psychological fact. Do you not mean, then, that you are going to ask about the psychological operations necessary to handle number, and not about the psychology of number itself? No, I reply, I do not mean that; I mean that even if number were a thousand times a quality of objects in themselves (and that is a metaphysical question which does not concern us) still number as learned, as appropriated by a pupil, must be a construction of his own mind. Number as an absolute fact is a thing about which the teacher need not concern himself, but number as meaning something to the child's mind must be both an operation and a product of his mind. All the best modern pedagogy rests on the supposition that not even a sense-quality, like a color or a sound, is simply a quality of a thing, bat is primarily an activity of the brain and of the sense organ; something which the child does through eye or ear. If this is so, we may be sure that so complex a thing as number, is, educationally, a mental activity. If a savage race cannot count more than four, if an Indian will not do his trading in bulk, but insists that for every skin bought of him two dollars (or whatever) be laid down by its side, and so on, the reason must be mental, not physical. If any one insists that, say, three is a thing, or a property of a thing and requires no mental operation, not even he will hold that "third" is a physical fact, and yet the idea of third plays just as important a part in arithmetical operations as does that of three. I should like to see what any one who denies the psychological character of number would do with fractions-with the fact that four quarters are always as many as four whole ones, and may be as much, when the mental standard of reference, the unit of measurement, varies, as from feet to yards. If number does not itself involve a psychological operation, how does it happen that if I have four dollars, each dollar is onefourth, but if I have five, each of those same dollars is only onefifth ? Psychological Character of Number. But it is advisable to show what, in particular, is the psychological character of number. In most generic terms, number is the mental act of analysis-synthesis reduced to its simplest and, therefore, most formal terms. According to the best psychology, every mental act is a synthetic-analytic operation; it involves, therefore, both discrimination and unification, and these not in succession, but together, though one of them may, of course, be more prominent than the other. Suppose a child sees a ball for the first time, and by seeing I mean not merely that his eyes rest upon it, but that he gets hold of it mentally as an object, however defective his idea may be. Here is synthesis; all the qualities are held together in a unity, otherwise it would not be a ball, an object at all. But there is equally analysis; some trait, some quality must stick out in the child's mind, or else the ball would not be different to him from his mother's face, or from his own foot. The roundness of it, the delightful fact that it can be thrown, that it will bound, some such distinctive mark must stand out. An object has identity to us only through some distinct quality, but this quality belongs to an individual or whole thing. Psychologically, there is no difference between the act of identifying discrimination, of analysis-synthesis, performed by the child in recognition of a ball, and the highest scientific flight, save in degree. Later steps only bring into distinct consciousness what the identified whole is and just what trait is necessary to mark it off from all others. It is this continuity of process between the lowest attainment and the highest which gives at once the greatest encouragement to the teacher, and supplies him with the deepest warning. It encourages because it shows the far-reaching consequences of the simplest act, when performed right, performed in accordance with the normal psychical operation. Performed |